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Metamath Proof Explorer

Theorem elelsuc

Description: Membership in a successor. (Contributed by NM, 20-Jun-1998)

		Ref	Expression
	Assertion	elelsuc	$⊢ A \in B \to A \in suc B$

Step	Hyp	Ref	Expression
1		orc	$⊢ A \in B \to (A \in B \lor A = B)$
2		elsucg	$⊢ A \in B \to (A \in suc B \leftrightarrow (A \in B \lor A = B))$
3	1 2	mpbird	$⊢ A \in B \to A \in suc B$